Novel full-field Mueller-matrix tomography will be implemented to measure Mueller matrices of intact biological tissues with both depth and lateral resolution in microscopic scales. The system is based on optical coherence tomography (OCT) and polarimetry. Mueller-matrix tomograms, measured by varying the polarization states of the source beam and the reference beam, completely characterize the polarization properties of the samples. The polarization properties can be very sensitive to the physiological states of biological tissues. The initial experimental results presented here `demonstrated Mueller-matrix tomography for the first time and indicated that this new approach reveals some tissue structures that are not observable by the conventional OCT. However, the initial experimental setup is too slow for soft-tissue imaging. The proposed new setup is capable of real-time measurements. Specifically, a CCD camera will provide full-field measurements, while computer-controlled liquid-crystal retarders will automatically vary the polarization states of the source and reference arms. The system will be coordinated to implement the novel "synchronous-illumination" lock-in technique. The proposed setup will be tested by studying biological tissues in vitro. Mueller-matrix tomograms and the corresponding polarization parameters including bireffingence, diattenuation, and depolarization will be investigated. The proposed setup will also be tested by recording the time course of tissue coagulation because it is known that coagulation reduces tissue birefingence. The advantages of the proposed technology include: 1) A complete characterization of biological polarization with depth resolution; 2) Sensitive optical contrast; 3) High imaging resolution; 4) Real-time image acquisitions; and 5) Non-invasive use of non-ionizing radiation. Optical tomography in biological tissues is very challenging because light is strongly scattering in tissues. OCT was designed to meet this challenge, and the proposed Mueller-matrix OCT adds a new dimension to OCT. The proposed technology will potentially find broad applications in medical diagnostics for superficial lesions such as ocular, skin, and cervical lesions.